Processing Vector Fields

In my PhD research, I had to deal with a lot of data.  Particularly with movies of particles moving around in water. These movies were processed, via Particle Image Velocimetry, to give vector fields of the velocity in the flow.  For an example, here’s some rough data that I took of a cylinder in flow, presented as colored images instead of thousands of tiny arrows:

The black part is masking out the cylinder and its shadow. The top half shows the horizontal velocity (with the incoming flow subtracted), and the bottom half is the vertical velocity.  Together, these show the wake flapping, and vortices shedding from the back. For the curious, the cylinder is in a water tunnel with a freestream velocity is 0.41 m/s, and has a radius of 6 mm. The diameter-based Reynolds number is about 4900. The video above has a frame rate of 1.76 frames per convective time unit.

Once I had the vector fields, then it’s a question of what knowledge to extract from the flow. For example, are there vortices? Are there any repeating patterns of activity? What if we assume that any patterns change harmonically?

First, it’s worth looking at the average flow field. The color shows the speed, and the arrows show the local flow directions. The velocity is scaled by the freestream speed.

This shows that the flow speeds up along the sides of the cylinder, and slows down behind it. Pretty much what you’d expect.

How about the dynamics? The simplest thing is to count the flapping rate of the flow. We find that it oscillates with a Strouhal number of about 0.17. This is basically what’s expected for a cylinder.

Beyond that? We’ll have to do some fancy things. I’ll make separate articles for different approaches: Fourier analysis, POD, DMD, and more!

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